Answer to Question #327665 in Statistics and Probability for WIL

Question

Five hundred tickets will be sold and these will be raffled during the town fiesta. One of these tickets will win Php 3,000 and the rest will win nothing. What will be the expected outcome and variance of your gain if you will buy one of the tickets?

Answer 1

Let the random variable X be the random of the amount won. The random variable X may take on only two value, (0,3000). That is x=0,3000

There are five hundred tickets to be sold and only one ticket wins P3,000. Therefore, the probability that a ticket wins P3,000 is 1/500

and the probability that a tickets wins nothing is 2-1/500=499/500

We can write this as, p(x=0)=499/500

and p(x=3000)=1/500

The expected value is given as,

$E(x)=\sum P(x)x=(0)(499/500)+(3000)(1/500)=6$

To find the variance, we first find

$E(x^2)=\sum P(x)x^2=(3000^2) (1/500)=18000$

Variance,

$var(x)=E(x^2)-(E(x))^2=18000-36=17964$

The expected gain and the variance of your gain are 6 and 17964 respectively.